The lines ${{l}_{1}}$ and ${{l}_{2}}$ have equations $\mathbf{r}=\overrightarrow{OA}+\lambda \left(

Question

The lines ${{l}_{1}}$ and ${{l}_{2}}$ have equations $\mathbf{r}=\overrightarrow{OA}+\lambda \left( \begin{matrix} 1 \-1 \5 \\end{matrix} ight)$ and $\mathbf{r}=\overrightarrow{OB}+\mu \left( \begin{matrix} 2 \1 \ 1 \\end{matrix} ight)$, $\lambda $, $\mu \in \mathbb{R}$ respectively, where $\overrightarrow{OA}=\left( \begin{matrix} 1 \ 2 \ -1 \\end{matrix} ight)$, $\overrightarrow{OB}=\left( \begin{matrix} 2 \ 4 \-5 \\end{matrix} ight)$. The lines ${{l}_{1}}$ and ${{l}_{2}}$ intersect at point $C$. Find the position of vector of $C$. [3] Given that $\overrightarrow{AB}$ is perpendicular to ${{l}_{2}}$, find the equation of the reflection of ${{l}_{1}}$ in ${{l}_{2}}$. [4]

Accepted Answer

l₁ and l₂ do not intersect (parallel lines); A' = (3, 0, -5); Line: r = (1,2,-5) + α(1,-1,-1)

2011 MJC P1 Q7 (i)(ii)

2011 MJC P1 Q7 (i)(ii)

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